Electron Bernstein waves are analyzed as possible candidates for heating spherical tokamaks. An inhomogeneous plane slab model of the plasma with a sheared magnetic field is used to calculate the linear conversion of the ordinary mode (O-mode) to the extraordinary mode (X-mode). A formula for the fraction of the incident O-mode energy which is converted to the X-mode at the O-mode cutoff is derived. This fraction is then able to propagate to the upper hybrid resonance where it is converted to the electron Bernstein mode. The damping of electron Bernstein waves at the fourth harmonic resonance, corresponding to a 60 GHz source on the Mega Amp Spherical Tokamak MAST [A. C. Darke et al. , Proceedings of the 16th Symposium on Fusion Energy, Champaign-Urbana, Illinois (IEEE, Piscataway, NJ, 1995, Vol. 2, p. 1456)], is computed. For comparison, results are also presented for a lower frequency source, close to the fundamental electron cyclotron resonance. Both the fundamental and the fourth harmonic are shown to be so strongly absorbing that the electron Bernstein wave would be totally absorbed in the outer regions of the resonance. This feature implies that electron Bernstein wave current drive (on- or off-axis) could be very efficient.